A project manager is in charge of 3 ongoing projects, A, B, and C. Due to recent reorganization, the project manager can assign additional employees to the 3 projects. Each employee who is assigned to a project can reduce the time to complete the project. The table below summarizes the data for the 3 projects. For instance, at most 5 employees may be assigned to project A. Each employee assigned to project A reduces the completion time by 3 days. (For example, if 3 employees are assigned to project A, its completion time is reduced by 9 days.) Total 11 employees are available. The project manager must maximize the least reduction among all 3 projects. For instance, if we can reduce the completion time of projects A, B, and C by 6, 8, and 9 days, respectively, the least reduction among all 3 projects is 6 days. Please formulate an LP model that helps the project manager assign the 11 employees. Projects Maximum Number of Employees Reduction of Completion Time (days / employee) A B 5 6 3 4 C 4 3
A project manager is in charge of 3 ongoing projects, A, B, and C. Due to recent reorganization, the project manager can assign additional employees to the 3 projects. Each employee who is assigned to a project can reduce the time to complete the project. The table below summarizes the data for the 3 projects. For instance, at most 5 employees may be assigned to project A. Each employee assigned to project A reduces the completion time by 3 days. (For example, if 3 employees are assigned to project A, its completion time is reduced by 9 days.) Total 11 employees are available. The project manager must maximize the least reduction among all 3 projects. For instance, if we can reduce the completion time of projects A, B, and C by 6, 8, and 9 days, respectively, the least reduction among all 3 projects is 6 days. Please formulate an LP model that helps the project manager assign the 11 employees. Projects Maximum Number of Employees Reduction of Completion Time (days / employee) A B 5 6 3 4 C 4 3
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Transcribed Image Text:**Transcription for Educational Website:**
A project manager is in charge of 3 ongoing projects, A, B, and C. Due to recent reorganization, the project manager can assign additional employees to the 3 projects. Each employee who is assigned to a project can reduce the time to complete the project. The table below summarizes the data for the 3 projects. For instance, at most 5 employees may be assigned to project A. Each employee assigned to project A reduces the completion time by 3 days. (For example, if 3 employees are assigned to project A, its completion time is reduced by 9 days.) A total of 11 employees are available. The project manager must maximize the least reduction among all 3 projects. For instance, if we can reduce the completion time of projects A, B, and C by 6, 8, and 9 days, respectively, the least reduction among all 3 projects is 6 days. Please formulate an LP model that helps the project manager assign the 11 employees.
**Table:**
| Projects | A | B | C |
|----------|---|---|---|
| Maximum Number of Employees | 5 | 6 | 4 |
| Reduction of Completion Time (days/employee) | 3 | 4 | 3 |
**Explanation:**
This table outlines the constraints and reduction rates for assigning additional employees to projects A, B, and C:
- **Maximum Number of Employees:** Project A can have up to 5 employees, Project B can have up to 6, and Project C can have up to 4.
- **Reduction of Completion Time (days/employee):** Each employee assigned to a project reduces its completion time. For Project A, each employee reduces the time by 3 days, Project B by 4 days, and Project C by 3 days.
The goal is to employ a Linear Programming (LP) model to optimize the assignment of the available 11 employees to maximize the minimum reduction in completion times across all projects.
Expert Solution

Step 1: Decision varaibles
Let,
A = Number of employees assigned to Project A
B = Number of employees assigned to project B
C = Number of employees assigned to project C
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